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Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination
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Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination

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  • Sebastian Grauwin

    (University of Lyon, Lyon, F-69003, France; ENS-LYON, Laboratoire de Physique, UMR 5672, Lyon, F-69007, France, Institut rhonalpin des systemes complexes, IXXI, Lyon, F-69007, France)

  • Florence Goffette-Nagot

    (University of Lyon, Lyon, F-69003, France; CNRS, UMR 5824, GATE, Ecully, F-69130, France; ENS LSH, Lyon, F-69007, France)

  • Pablo Jensen

    (University of Lyon, Lyon, F-69003, France; CNRS, LET, UMR 5593, Lyon, F-69363 France, ENS-LYON, Laboratoire de Physique, UMR 5672, Lyon, F-69007, France, Institut rhônalpin des systèmes complexes, IXXI, Lyon, F-69007, France)

Abstract

In his 1971's Dynamic Models of Segregation paper, the economist Thomas C. Schelling showed that a small preference for one's neighbors to be of the same color could lead to total segregation, even if total segregation does not correspond to individual preferences and to a residential configuration maximizing the collective utility. The present work is aimed at deepening the understanding of the properties of dynamic models of segregation based on Schelling's hypotheses. Its main contributions are (i) to offer a comprehensive and up-to-date review of this family of models; (ii) to provide an analytical solution to the most general form of this model under rather general assumptions; to the best of our knowledge, such a solution did not exist so far; (iii) to analyse the effect of two devices aimed at decreasing segregation in such a model. Chapter one summarizes the ingredients of Schelling's models. We show how the choices of the agent's utility function, of the neighborhood description and of the dynamical rule can impact the outcome of a model. Based on the observation of simulations results, we find that the neighborhood description does not have a qualitative impact. As regards the dynamical rules, we show that the Logit Behavioral rule introduced in this literature by Young (1998); Zhang (2004b) presents several advantages relatively to the Best Response rule. Chapter two presents a general analytical solution to the model. To that aim, Schelling's model is recasted within the framework of evolutionary game theory, as previously done by Young (1998); Zhang (2004b). This allows to define sufficient assumptions regarding agents' utility functions that permit predicting the ï¬ nal state of the system starting from any conï¬ guration. This analytical resolution is then used to consider the outcomes of Schelling's utility function and of other utility functions previously used in this context. Chapter three examines the effects of introducing coordination in the moving decisions. This coordination is achieved through two different ways. We first impose different levels of taxes proportional to the externality generated by each move of the agents. It is shown that even a low level of tax is sufficient under certain circumstances to significantly reduce segregation. We then investigate the effect of the introduction of a local coordination by vote of co-proprietors, who are defined as the closest neighbors of each agent. It is shown that even a small amount of coordination can break segregation

Suggested Citation

  • Sebastian Grauwin & Florence Goffette-Nagot & Pablo Jensen, 2009. "Dynamic models of residential segregation: Brief review, analytical resolution and study of the introduction of coordination," Working Papers 0914, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    • Handle: RePEc:gat:wpaper:0914
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    1. Pancs, Romans & Vriend, Nicolaas J., 2007. "Schelling's spatial proximity model of segregation revisited," Journal of Public Economics, Elsevier, vol. 91(1-2), pages 1-24, February.
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    12. Carrington, William J & Troske, Kenneth R, 1997. "On Measuring Segregation in Samples with Small Units," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 402-409, October.
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    1. repec:hal:spmain:info:hdl:2441/5l6uh8ogmqildh09h5623b6bg is not listed on IDEAS
    2. Sylvain Barde, 2011. "Back to the future: a simple solution to schelling segregation," SciencePo Working papers Main hal-01069479, HAL.
    3. repec:spo:wpecon:info:hdl:2441/5l6uh8ogmqildh09h5623b6bg is not listed on IDEAS
    4. repec:spo:wpmain:info:hdl:2441/5l6uh8ogmqildh09h5623b6bg is not listed on IDEAS
    5. Philippe Collard, 2020. "Second-order micromotives and macrobehaviour," Journal of Computational Social Science, Springer, vol. 3(1), pages 209-229, April.
    6. Grauwin, Sébastian & Goffette-Nagot, Florence & Jensen, Pablo, 2012. "Dynamic models of residential segregation: An analytical solution," Journal of Public Economics, Elsevier, vol. 96(1), pages 124-141.
    7. repec:hal:wpspec:info:hdl:2441/5l6uh8ogmqildh09h5623b6bg is not listed on IDEAS

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    More about this item

    Keywords

    segregation; Schelling; potential function; coordination; tax; vote;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • J15 - Labor and Demographic Economics - - Demographic Economics - - - Economics of Minorities, Races, Indigenous Peoples, and Immigrants; Non-labor Discrimination

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